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    <title>函数间断点分类思维导图</title>
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</head>
<body>
    <div class="container">
        <header>
            <h1>函数间断点分类思维导图</h1>
            <p class="subtitle">全面解析函数间断点的分类体系、特征判断和应用实例</p>
        </header>
        
        <div class="mind-map">
            <!-- 中心节点 -->
            <div class="main-node">
                函数间断点分类
            </div>
            
            <!-- 第一层级 -->
            <div class="level-1">
                <!-- 第一类间断点 -->
                <div class="category">
                    <div class="category-node">
                        第一类间断点
                    </div>
                    <div class="level-2">
                        <div class="type-node">
                            <div class="type-title">可去间断点</div>
                            <div class="type-content">
                                <ul class="feature-list">
                                    <li><strong>特征：</strong>左右极限存在且相等</li>
                                    <li><strong>条件：</strong>f(x₀) ≠ 极限值 或 无定义</li>
                                    <li><strong>修复：</strong>重新定义 f(x₀)</li>
                                </ul>
                                <div class="example">
                                    例：f(x) = sin(x)/x 在 x=0 处
                                </div>
                            </div>
                        </div>
                        
                        <div class="type-node">
                            <div class="type-title">跳跃间断点</div>
                            <div class="type-content">
                                <ul class="feature-list">
                                    <li><strong>特征：</strong>左右极限存在但不相等</li>
                                    <li><strong>条件：</strong>limₓ→₀⁺ f(x) ≠ limₓ→₀⁻ f(x)</li>
                                    <li><strong>跳跃量：</strong>|右极限 - 左极限|</li>
                                </ul>
                                <div class="example">
                                    例：f(x) = |x|/x 在 x=0 处
                                </div>
                            </div>
                        </div>
                    </div>
                </div>
                
                <!-- 第二类间断点 -->
                <div class="category">
                    <div class="category-node second-class">
                        第二类间断点
                    </div>
                    <div class="level-2">
                        <div class="type-node second-class">
                            <div class="type-title">无穷间断点</div>
                            <div class="type-content">
                                <ul class="feature-list">
                                    <li><strong>特征：</strong>至少一侧极限为无穷大</li>
                                    <li><strong>条件：</strong>limₓ→₀ f(x) = ∞</li>
                                    <li><strong>图像：</strong>垂直渐近线</li>
                                </ul>
                                <div class="example">
                                    例：f(x) = 1/x 在 x=0 处
                                </div>
                            </div>
                        </div>
                        
                        <div class="type-node second-class">
                            <div class="type-title">振荡间断点</div>
                            <div class="type-content">
                                <ul class="feature-list">
                                    <li><strong>特征：</strong>函数值无限振荡</li>
                                    <li><strong>条件：</strong>极限不存在且不为∞</li>
                                    <li><strong>性质：</strong>取值稠密</li>
                                </ul>
                                <div class="example">
                                    例：f(x) = sin(1/x) 在 x=0 处
                                </div>
                            </div>
                        </div>
                    </div>
                </div>
            </div>
            
            <!-- 判断流程 -->
            <div class="judgment-flow">
                <div class="flow-title">间断点判断流程</div>
                <div class="flow-steps">
                    <div class="flow-step">
                        <strong>步骤1：</strong> 检查函数在 x₀ 处是否有定义
                    </div>
                    <div class="flow-step">
                        <strong>步骤2：</strong> 计算左极限 limₓ→₀⁻ f(x)
                    </div>
                    <div class="flow-step">
                        <strong>步骤3：</strong> 计算右极限 limₓ→₀⁺ f(x)
                    </div>
                    <div class="flow-step">
                        <strong>步骤4：</strong> 比较分析：
                        <ul class="feature-list">
                            <li>左右极限都存在 → 第一类间断点</li>
                            <li>左右极限相等 → 可去间断点</li>
                            <li>左右极限不等 → 跳跃间断点</li>
                            <li>至少一侧极限不存在 → 第二类间断点</li>
                            <li>趋于无穷 → 无穷间断点</li>
                            <li>振荡无极限 → 振荡间断点</li>
                        </ul>
                    </div>
                </div>
            </div>
            
            <!-- 性质对比表 -->
            <div class="comparison-table">
                <div class="table-title">间断点性质对比表</div>
                <table>
                    <thead>
                        <tr>
                            <th>类型</th>
                            <th>极限存在性</th>
                            <th>是否可修复</th>
                            <th>图像特征</th>
                            <th>典型例子</th>
                        </tr>
                    </thead>
                    <tbody>
                        <tr>
                            <td><strong>可去间断点</strong></td>
                            <td>存在</td>
                            <td>是</td>
                            <td>有"洞"</td>
                            <td>sin(x)/x (x=0)</td>
                        </tr>
                        <tr>
                            <td><strong>跳跃间断点</strong></td>
                            <td>左右存在但不相等</td>
                            <td>否</td>
                            <td>有"台阶"</td>
                            <td>|x|/x (x=0)</td>
                        </tr>
                        <tr>
                            <td><strong>无穷间断点</strong></td>
                            <td>不存在(∞)</td>
                            <td>否</td>
                            <td>垂直渐近线</td>
                            <td>1/x (x=0)</td>
                        </tr>
                        <tr>
                            <td><strong>振荡间断点</strong></td>
                            <td>不存在(振荡)</td>
                            <td>否</td>
                            <td>密集振荡</td>
                            <td>sin(1/x) (x=0)</td>
                        </tr>
                    </tbody>
                </table>
            </div>
            
            <!-- 记忆口诀 -->
            <div class="mnemonic">
                <div class="mnemonic-text">
                    "左右相等是可去，左右不等是跳跃；<br>
                    趋于无穷第二类，振荡无极限也是它。"
                </div>
            </div>
        </div>
    </div>
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